Direction: Find the first derivative of the following functions: 1. y = sin (2x) - cos (2x) 2. y = tan x + cot x cos x 3. у%3D tan (3х)cot (3x) 4. у 3 1+sin x

Q: Given the function f(x,y)=3x² - y over the rectangular region, R = {(x, y): 0 < x s2,0 < y s 3}.…

A: we know, ∬Rfx,ydA=∫03∫02fx,ydxdy

Q: Use implicit differentiation to find dz/dx and dz/dy. yz = 2 In(x + z) dz ax ze dy II II

A: Consider a function f(x,y,z) .Then to find ∂f∂x ,differentiate f with respect to x taking y and z as…

Q: ) y^2=(x^2 - 9)/(x - 4) b) y^2= (x^2 + 2x)/ x-1 find the x and y intercept, symmetry,…

A: Given

Q: Assume f and g are differentiable functions with h(x) = f(g(x)). Suppose the equation of the line…

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Q: Q fin) the Area of Regian R 2. /4

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Q: Solve the differential equation: dx+(x-y+2)^2dy=0

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Q: Astivity 3 tind the dertve of 2メー3 う×ース enuing the definitiom -

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Q: (2х — Зу + 1)dх — (3х + 2у — 4)dy %3D 0

A: To solve the given first order differential equation.

Q: 2. y' + xy = xy

A: Find your answer below

Q: a + 2b – c + 4d = 1 -a – 3b + 2c + 2d = 4 2a + 2b – c + 2d = 2 a + 2b +c = 1 using, a. Cramer's Rule

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Q: The width of a rectangle is increasing at a rate of 5 cm/sec, while the length increases at 6…

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Q: Find the point(s) of intersection (if any) of the plane and the line. (If an answer does not exist,…

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Q: Find the volume of the solid generated by revolving the area of circle: (x-2)²+y²=4; about the x…

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Q: Find parametricequations of the line that satisfies the stated conditions. The line through (8, 5)…

A: The vector equation of line L, passing through the point x0,y0 and parallel to the vector b=li+mj is…

Q: Find the mass of the solid bounded by the ry-plane, yz-plane, xz-plane, and the plane (z/3) + (y/4)…

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Q: d Use the table below to find [g(x) – f(x)]| dx |x=2 1 2 4 f'(x) gʻ(x) 4 1 2 1 2 4 d [g(x) – f(x)1]…

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Q: 1と 8t y=x?+4 ソニx? ー4 4

A: The region is bounded by the curves y=x2+4 and y=x2 from x=-4 to x=4revolved about x-axis

Q: A function f is defined by f(x)=x' – 3x² – 24x , where xeR. (i) Find the coordinates of the…

A: Given that fx=x3-3x2-24xi  stationary points occurs…

Q: Use Wallis' formula to evaluate ? cosxsin²xdx 2

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Q: Find the gradient of the function at the given point. w = x tan(y + z), (13, 14, –12) Vw(13, 14,…

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Q: Find the 24th derivative of y = -sinx

A: Topic = Derivative    The 24th derivative isy24 =-sinx

Q: Cost 3x dх

A: The objective of the question is evaluate the indefinite integral.

Q: Exact Equation Solution of (2xy -tany) dx + (x^2 - xsec^2 y) dy =0 Answer: x^2y−xtany=c

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Q: The shaded region shown below is bounded by the functions f (x) = -x2 +1.5x + 10 and g(x) = -x + 8,…

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Q: Find the area of the shaded region. r = 3+2 cos 0 r = sin 20

A: Area of polar region =                                    integration of r^2/2 d(theta)

Q: (x, y, z) =

A: Follow the procedure given below.

Q: Find the Cartesian equation of the parametric equations x = a cost y = b sint 0<t< and identify its…

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Q: Consider the one-parameter family of linear systems depending on the parameter a. dY This family…

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Q: 00 Expand the function in a power series a,x" with center c 0. Find a,x". 8+7x

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Q: (x+1)* 40. k! k=0 IM:

A: The given power series      ∑k=0∞x+1kk!

Q: Evaluate the limit of f(x) numerically or state that the limit does not exist. 5x? – 180 f(x) = x +…

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Q: Find the point(s) of intersection (if any) of the plane and the line. (If an answer does not exist,…

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Q: In each part, use a scalar triple product to determine whether the vectors lie in the same plane.…

A: a) u=2,-2,2, v=3,0,-2, w=5,-2,0u.v×w=2-2230-25-20u.v×w=2(10)+2(-4-6)u.v×w=20-20u.v×w=0Since ther…

Q: Question The base of a triangle is shrinking at a rate of I1 cm/s and the height of the triangle is…

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Q: Evaluate the integral by any method. NOTE: Enter the exact answer. d.x V4 - 3x16

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Q: Find the volume of the solid generated by revolving the region bounded by x2/3 + 1,0 < < 8, about…

A: Follow next step

Q: dy Solve the following differential equation: x+ y = 4x dx

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Q: Evaluate the limit, if it exists. (Use symbolic notation and fractions where needed. Enter "DNE" in…

A: Given,            limx→4x-2x-4

Q: In each part, use a scalar triple product to determine whether the vectors lie in the same plane.…

A: This question is related to vectors, we will solve it solve it using given information.

Q: complete and detailed solution using techniques of variation

A: Given,            ∫dy1+y+13

Q: A car's movement is represented by the function 2x3 + 6x2 + 2x + 3 in kilometers reco at an hourly…

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Q: III. SOLVE THE FOLLOWING INDETERMINATE FORMS(: |2 + x² 2) Lim

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Q: Determine whether the lines intersect, and if so, find the point of intersection. (If an answer does…

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Q: Insert 4 arithmetic means between 1 and 15. (b) Insert 5 geometric means between 3 and 192.

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Q: 5.SUPPOSE tu at fex)= XJgcK)· If 903)=16 and g C3)=-5.what is f'(3)?

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Q: Find the area of the surface obtained by rotating the curve x = 3 (y + 2)3/2, 1 <y< 2, about the…

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Q: Find parametric equations for the line whose vector equation is given (а) (г, у) — (6, —5) + t(1,…

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Q: 4x+1 b. g(x) 9x-2

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Q: B. If the measure of arc AB is 50 degrees, what is the measure of angle ADB? O 25 degrees 90 degrees…

A: As we know the degree of the arc is equal to the measure of the central angle that creates the arc.…

Q: Consider the following planes. Sx+ 6y -2= 66 x- 12y + 22 0 (a) Find the angle between the two…

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